Time-dependent He-McKellar-Wilkens effect on noncommutative space

In this paper, we study time-dependent He-McKellar-Wilkens (HMW) phase shift, as well as its extension on noncommutative space. We show that for adiabatic varying external magnetic field, the original HMW effect can receive a time-dependent correction. The adiabatic approximation is valid if frequency of the varying external field is smaller enough than the one by which the spinor particle takes a single round. Noncommutative corrections are studied by using Seiberg-Witten map such that the final results are gauge invariant. We find that there are two kinds of contributions, one is purely adiabatic, and the other one is a constant correction and depends on frequency of the external field.